By the Numbers
This illustrated trek ventures into the realm of numbers, as revealed in mathematics, science, literature, and art. It offers glimpses of the enduring appeal of integers, primes, partitions, pi, Fibonacci numbers and the golden ratio, hailstone numbers, Pascal's triangle, and other quirky and fascinating denizens of numeropolis.
Online Bibliography
Integers
Applegate, D., and J.C. Lagarias. Preprint. Lower bounds for the total stopping time of 3x + 1 iterates.
Dewdney, A.K. 1988. How to pan for primes in numerical gravel. Scientific American 259(July):90-93.
Gardner, M. 1964. The remarkable lore of the prime numbers. Scientific American 210(March):120-128.
Krasikov, I., and J.C. Lagarias. Preprint. Bounds for the 3x + 1 problem using difference inequalities.
Peterson, I. 2002. Taxicab numbers. MAA Online (July 29).
______. 2002. Dangerous problems. MAA Online (July 1).
______. 2002. Prime spirals. MAA Online (May 6).
______. 2000. The power of partitions. Science News 157(June 17):396-397.
______. 1997. Winning partitions. MAA Online (March 22).
Pickover, C. 1991. A prime plaid. In Computers and the Imagination: Visual Adventures Beyond the Edge. New York: St. Martin's.
Silverman, J.H. 1993. Taxicabs and sums of two cubes. American Mathematical Monthly 100(April):331-340.
Stein, M.L., S.M. Ulam, and M.B. Wells. 1964. A visual display of some properties of the distribution of primes. American Mathematical Monthly 71(May):516-520.
Wolfram MathWorld: Collatz Problem
Wolfram MathWorld: Taxicab Number
Patterns in the Mysterious Hailstone (3n + 1) Numbers
Cliff Pickover
Pi
Bailey, D.H., J.M. Borwein, P.B. Borwein, and S. Plouffe. 1997. The quest for pi. Mathematical Intelligencer 19(No. 1):50-57.
Beckmann, P. 1971. A History of Pi. New York: St. Martin's Press.
Blatner, D. 1997. The Joy of Pi. New York: Walker.
Dudley, U. 1992. Legislating pi. In Mathematical Cranks. Washington, D.C.: Mathematical Association of America.
Gardner, M. 1999. Slicing pi into millions. In Gardner's Whys & Wherefores. Amherst, N.Y.: Prometheus Books.
Keith, M. 1999. The pi code.
______. 1999. Lady pi.
Peterson, I. 2002. A trillion pieces of pi. MAA Online (Dec. 16).
______. 2001. Pi à la mode. Science News 160(Sept. 1):136-137.
______. 2000. The incredible pi code. MAA Online (April 1).
______. 2000. Sliding pi. MAA Online (June 5).
______. 1999. A song about pi. MAA Online (July 12).
______. 1998. Pick a digit, any digit. MAA Online (March 2).
______. 1996. A passion for pi. MAA Online (March 11).
Singmaster, D. 1985. The legal values of pi. Mathematical Intelligencer 7(No. 2):69-72.
Watson, B. 2000. Squaring the circle is no piece of pi. Smithsonian 31(May):71-82.
Indiana bill sets the value of pi to 3
Alex Lopez-Ortiz, University of Waterloo
Fibonacci Numbers and the Golden Ratio
Benjamin, A.T., and J.J. Quinn. 2003. Proofs That Really Count: The Art of Combinatorial Proof. Washington, D.C.: Mathematical Association of America.
Brown, D. 2003. The Da Vinci Code. New York: Doubleday.
Devlin, K. 2004. Cracking the The Da Vinci Code. Discover 25(June).
______. 2004. Good stories, pity they're not true. MAA Online (June).
______. 2002. The 800th birthday of the book that brought numbers to the west . MAA Online (October).
Elam, K. 2001. Geometry of Design: Studies in Proportion and . New York: Princeton Architectural Press.
Klar, A.J.S. 2002. Plant mathematics: Fibonacci's flowers. Nature 417(June 6):595.
Livio, M. 2002. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books.
Markowsky, G. 1992. Misconceptions about the golden ratio. College Mathematics Journal 23(January):2-19.
Naylor, M. 2002. Golden, sqrt[2], and pi flowers: A spiral story. Mathematics Magazine 75(June):163-172.
Peterson, I. 2004. Counting on Fibonacci. MAA Online (May 3).
______. 2002. A Fibonacci fountain. MAA Online (Oct. 21).
______. 2002. Stepping beyond Fibonacci numbers. MAA Online (Sept. 30).
______. 2002. Golden blossoms and pi flowers. MAA Online (Sept. 2).
______. 2001. Fibonacci's Chinese calendar. MAA Online (Feb. 5).
Wolfram MathWorld: Fibonacci Number
Biography: Fibonacci.
Fibonacci Numbers and the Golden Section
Ron Knott, University of Surrey
Fibonacci Numbers in Nature
Jill Britton, Camosun College
Pascal's Triangle
Peterson, I. 2003. Sound-byte math music. MAA Online (Jan. 6).
______. 1997. Pascal's fractals. MAA Online (Feb. 10).
Math Forum: Pascal's Triangle
National Curve Bank: Pascal's Triangle in Needlepoint
Origami: Pascal Triangle Instructions
Helena Verrill
Pascal's Triangle and Its Patterns
Pascal's Triangle from Top to Bottom
Wikipedia: Pascal's Triangle
Wolfram MathWorld: Pascal's Triangle
Books
Adams, C., and T. Garrity. 2007. The Great pi/e Debate. Mathematical Association of America (DVD).
Conway, J.H., and R.K. Guy. 1996. The Book of Numbers. Springer.
Enzensberger, H.M. 2000. The Number Devil: A Mathematical Adventure. Holt.
Flannery, D.A. 2006. The Square Root of 2: A Dialogue Concerning a Number and a Sequence. Springer.
Maor, E. 1998. e: The Story of a Number. Princeton University Press.
Pasles, P.C. 2007. Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey. Princeton University Press.
Reid, C. 2006. From Zero to Infinity: What Makes Numbers Interesting. A K Peters.
Wells, D. 1998. The Dictionary of Curious and Interesting Numbers, rev. ed. Penguin.
